Fraction Operations
Lessons in this chapter
About Fraction Operations
Fraction Operations is where fractions become something to calculate with, and the first rule is the one kids resist: only like parts can be added.
Add and Subtract Fractions with the Same Denominator sets the rule. Two fifths plus one fifth is three fifths, with the denominator unchanged, because you are counting fifths. The classic error, adding the denominators to get three tenths, comes from treating the fraction as two separate numbers.
Decompose Fractions and Mixed Numbers breaks a fraction into parts, so seven quarters becomes four quarters plus three quarters, which is one and three quarters. This is the conversion between improper fractions and mixed numbers, derived rather than memorized.
Compare and Order Improper Fractions extends the comparison work to fractions past 1, where a quick check against the whole number often settles it before any common denominator is needed.
Add, Subtract and Multiply Fractions and MIxed Numbers closes the chapter. Multiplication is the surprise: multiplying two fractions is easier than adding them, since you multiply across without needing a common denominator, and the result being smaller than both is the part worth explaining.
Add and Subtract Fractions with the Same Denominator, Decompose Fractions and Mixed Numbers and Compare and Order Improper Fractions each open as a worksheet in the page. The chapter starts with adding fractions with like denominators, and every question is marked as you work it. All four lessons are free to try, with no login needed for your first 3.
Frequently asked questions
Add and Subtract Fractions with the Same Denominator sets the rule that only like parts can be counted together, and Decompose Fractions and Mixed Numbers derives the conversion between improper fractions and mixed numbers rather than asking for it to be memorized. Compare and Order Improper Fractions extends the comparison work past 1, and the last lesson adds multiplying fractions and mixed numbers. The chapter sits in Number and Operations with Fractions (4.NF).
Because the denominator names the size of the pieces, not a quantity. Two fifths plus one fifth is three fifths, the same way two apples plus one apple is three apples.
Decompose it into wholes plus a remainder. Seven quarters is four quarters, which is 1, plus three quarters, so it is one and three quarters.
Because no common denominator is needed. Multiply the numerators and the denominators, and that is the answer.
Because you are taking a part of a part. Half of a third is a sixth, which is smaller than either, and that only feels wrong because whole-number multiplication always grows.
A whole number and a fraction written together, like one and three quarters. It is the same value as the improper fraction seven quarters.